Blender 2.8 repair mesh
There was some manual work to do. I don't know how useful this answer is, but my steps were:


S.001 Bring the object to a sensible scale, and apply the scale.
In the 3D View 'View' tab, set Near and Far Clipping to be able to see the object consistently
Note, by enabling Face Normals in Overlays, that the object is already 2-sided
Also note, by seeing the face-dots around the perimeter, that there are degenerate faces connecting the inside and outside.


So.


ShiftG select the degenerate faces by similar area (0). Delete them.
Using CtrlL select (linked) all the inside faces and delete them.
Delete the bottom half of the object and replace with a Mirror modifier in Z, 'Merge' and 'Clip' checked.
Assign a Solidify modifier above the Mirror with 'Rim' unchecked to allow merging, towards the inside. This leaves  gaps which can be filled, but no intersecting faces, which you're trying to avoid.
When it looks good, apply the modifiers.
Enable the 'F2' shipped Add-On.  and use it to run round the gaps between edges, connecting by hand, (holding down F), because 'Bridge Edge Loops' fails somewhere, and I want to see where.
OK, got them, fix the topology at the points by hand. About half a dozen faces.




Bevel and subdivide, if wanted.